Mathematical theory of epidemics and pandemics based on the laws of chain and thermal explosions

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Abstract

The article presents a theory of the spread of the virus, including epidemics and pandemics, based on the theories of chain and thermal explosions, where two parameters were introduced to simulate the spread of the virus in an isolated community of people. A model of a community in the form of a multilayered bulb is proposed, in which the infection process proceeds in layers. The formulas obtained correlate with good accuracy with statistical data on the spread of the virus at stable stages of the pandemic. The validity of the model is confirmed by a combination of the formulas obtained, with a number of simplifications, with the formulas of the chain explosion theory and others. The presented theory is in qualitative agreement with empirical theories – SIR, SIRS and others.

The model may be interesting for epidemiology and exact science, since formulas with new parameters may be in demand for modeling phenomena in other areas of nature. The article shows the connection between the theories of chain and thermal explosions.

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About the authors

A. A. Philippov

Federal Research Center of Chemical Physics named after N.N. Semenov of the Russian Academy of Sciences

Author for correspondence.
Email: 7987961@mail.ru
Russian Federation, Moscow

References

  1. Семенов Н.Н. Цепные реакции. Л.: ОНТИ, 1934. С. 110.
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  4. Philippov A.A., Khalturinskiy N.A. To the theory of ignition by a hot surface: critical conditions for occurrence of explosive and avalanche-like processes. Zeldovic memorial, 2015. V. 2.
  5. Филиппов А.А., Берлин А.А. Математическая теория зажигания накаленной поверхностью // Доклады РАН. Физика. Технические науки. 2022. Т. 503. № 1. С. 28–34.
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  7. Гольдберг В.И. Развитие цепной модели динамики распространения пандемии COVID-19 // Горение и взрыв. 2021. Т. 14. № 3. С. 3–10.

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2. Fig. 1. The increase in the number of cases in Moscow during the new wave of virus spread 09.10.2020–10.01.2021, in logarithmic coordinates from time, in accordance with equation (25), in which statistical data (points) fall on a theoretical straight line, with linear dependence: y ≈ 0.0353x – 9.747. The optimal number of Na ≈ 790,000 people was found in the calculations, and Ni was counted from the beginning of the wave occurrence from 09.10.2020.

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